Creating a compelling haptic sense of immersion in a virtual environment is a challenging task for the control engineer. A haptic display must render both low impedance free-space motion and high impedance rigid constraints while ensuring stable interaction. This paper outlines a control design approach for the most common haptic display implementation, the impedance display. Two-port absolute stability criteria are used to develop explicit design bounds for virtual coupling networks which guarantee system stability for a broad class of human operators and virtual environments. The technique is applied to the Excalibur three-axis force display. The resulting absolutely stable haptic interface is the centerpiece of a virtual building block simulation which emulates the behavior of LEGO/sup TM/ bricks in a virtual environment.